Rotational cavity optomechanics

TL;DR

This paper presents a theoretical study of how a rotating nanoparticle interacts with an optical cavity mode carrying orbital angular momentum, enabling precise measurement of its rotation frequency through Doppler shifts.

Contribution

It introduces a novel method to detect nanoparticle rotation frequency via Doppler shifts in an orbital angular momentum-carrying optical cavity, with analysis of linear and nonlinear response regimes.

Findings

Rotation frequency imprints on probe optical mode via Doppler shift

Optical probe's effect vanishes in linear response, enabling accurate measurement

Measurement accuracy degrades in the nonlinear regime

Abstract

We theoretically examine the optomechanical interaction between a rotating nanoparticle and an orbital angular momentum-carrying optical cavity mode. Specifically, we consider a dielectric nanosphere rotating uniformly in a ring-shaped optical potential inside a Fabry-Perot resonator. The motion of the particle is probed by a weak angular lattice, created by introducing two additional degenerate Laguerre-Gaussian cavity modes carrying equal and opposite orbital angular momenta. We demonstrate that the rotation frequency of the nanoparticle is imprinted on the probe optical mode, via the Doppler shift, and thus may be sensed experimentally using homodyne detection. We show analytically that the effect of the optical probe on the particle rotation vanishes in the regime of linear response, resulting in an accurate frequency measurement. We also numerically characterize the degradation of the measurement accuracy when the system is driven in the nonlinear regime. Our results are relevant to rotational Doppler velocimetry and to studies of rotational Brownian motion in a periodic lattice.